Problem: Solve for $x$ : $x^2 - 15x + 56 = 0$
Solution: The coefficient on the $x$ term is $-15$ and the constant term is $56$ , so we need to find two numbers that add up to $-15$ and multiply to $56$ The two numbers $-7$ and $-8$ satisfy both conditions: $ {-7} + {-8} = {-15} $ $ {-7} \times {-8} = {56} $ $(x {-7}) (x {-8}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -7) (x -8) = 0$ $x - 7 = 0$ or $x - 8 = 0$ Thus, $x = 7$ and $x = 8$ are the solutions.